For questions regarding the mathematical analysis of voting systems and behavior. Examples include the median voter theorem or the Condorcet jury theorems.

learn more… | top users | synonyms

1
vote
0answers
27 views

What is a good introductory book on Rational Choice Theory for a mathematician?

I'm interested in Rational Choice Theory as an approach to political science. Amongst other, related subjects, I'd like to know a thing or two about Arrow's impossibility theorem (and other aspects of ...
-1
votes
1answer
43 views

Arrow's impossibility theorem implications [closed]

If we knew that in an unfair voting system (ie: it is known that IIA does not hold) then if (1) holds, how would we go about inferring that (2) holds and then is it possible to show that if (1) and (2)...
0
votes
1answer
28 views

Poisson vs Binomial for Voting

(this is my first post so I apologise if I am asking wrongly) I am trying to determine whether I should use poisson or binomial distribution to model american poll votes for the coming election. My ...
2
votes
2answers
29 views

Describe all irreducible voting systems with two outcomes

A situation where $n$ voters choose between two candidates can be modelized by a $n$-uple $(a_1,\ldots,a_n)\in\lbrace 0,1 \rbrace^n$, where $a_i$ denotes the wish of the $i$-th voter. So the voting ...
0
votes
1answer
29 views

Counterexample to each Arrow's axiom

I am trying to find ways that combine group preferences which hold for 3 out of the 4 Arrow's axioms. Here is what I have come up with so far: Unrestricted Domain Not sure what scheme would ...
4
votes
1answer
60 views

Analyse the US presidential election from the perspective of Arrow's theory

I want to consider the voting system against the 4 Arrow's axioms. So first the voting system simplifies to first-past-the post system where the highest polling candidate wins the election. How does ...
2
votes
1answer
20 views

name of a fairness criterion

I found the following fairness criterion in the exercises of Excursions in Modern Mathematics: If a majority of the voters have candidate X ranked last, then candidate X should not be a winner of the ...
0
votes
0answers
79 views

Advantages/disadvantages of a utiliarian social welfare function

If a planner obeys anonymity and strong Pareto principle (individual preferences carry over to the group), then the social utility function will be: $W(x)=\sum_{i=1, ..., n}U_i(x)$ i.e. summing ...
0
votes
0answers
8 views

Algorithm to determine popularity through sentiment, volume, time, and feedback

I am quite new to this space of ranking algorithms, and I'm faced with a problem. I have the following factors that will determine an entity's "popularity" ranking: Number of occurrences mentioned ...
0
votes
0answers
32 views

Show, by example, that we can find social welfare functions which satisfy any three of the four Arrow's axioms.

I want to show, by example, that we can find social welfare functions which satisfy any three of the four Arrow's axioms. Given at least three rewards, and at least two individuals, there is no ...
0
votes
1answer
30 views

Pairwise majority voting and Arrow's axioms

The following is a question on Arrow's theorem with a pairwise majority decision. The bits I was unsure about was (bi) (is the 4th condition satisfied?) and also is (bii) correct? Thanks for your help ...
0
votes
0answers
20 views

Sen's theorem on minimal liberalism

I want to solve the following question regarding Sen's theorem and preferences orderings. The bit I am having trouble with is 2b Question 1: Describe Sen's theorem ('paradox') There is no social ...
1
vote
1answer
30 views

Boolean functions and characters

I'm trying to solve this, but I have no idea how to start! I'm not even sure what the question is really asking. Can anybody rephrase this and perhaps give me pointers/solutions for one of the parts?
-1
votes
1answer
22 views

Condorcet winner in an examen subject with typo

I took a course in decisional models this semester. It is delightful because it allows to understand why are the weaknesses of every decision making process. Yet, the teacher gave us an old exam ...
7
votes
0answers
69 views

Can Continuous Time Markov Chains be used as a reasonable voting system?

I just compared a couple of example elections, as given on Wikipedia to show how Condorcet-methods differ from non-Condorcet ones, to what happens if you just interpret the underlying preference ...
3
votes
1answer
75 views

Algorithm for assigning users to “buckets” according to users' preferences and ranking

Suppose there is a set of $n$ users which must each be assigned to one, and only one, of $k$ mutually exclusive "buckets". However, the number of users allocated to the $i$-th bucket must be no lower ...
1
vote
2answers
39 views

IRV failing monotonicity criterion

I am looking for the simplest possible example of instant runoff voting failing the monotonicity criterion. By “simplest possible” I mean the scenario with the fewest number of candidates $(3)$ and ...
0
votes
1answer
27 views

Gaining intuition as to why maximal lotteries use randomness to break general ties

The maximal lottery is a voting system based on choosing an optimal candidate game-theoretically. If a winner isn't clear (there is no condorcet winner), then it will return probabilities as to which ...
0
votes
1answer
52 views

What is the strategy-proofness of maximal lottery?

The maximal lottery system is a voting system based in game theory. It is based in game theory. The general idea is that it is better than all the other voting systems. My question is, is it ...
0
votes
0answers
32 views

Voting Systems without tactical voting

Which voting systems do not have tactical voting? Specifically, expressing your true preference on a ballot will not result in a less favorably outcome. I'm looking at both multiple-winner and single-...
0
votes
0answers
14 views

For which voting system are multiple parties stable?

Most voting systems gravitate to two parties over time (namely, there is a bias to two candidates receiving a disportionate amount of votes.) For which voting systems does this not occur, i.e. ...
0
votes
0answers
18 views

Formula/theory to detect the desired number of workshop topics

I need to prepare a workshop and at the end of the workshop I want participants to choose from a set of questions (e.g. n=20) only x (e.g. x=5) questions to discuss. Therefore I want to give each ...
1
vote
0answers
22 views

Voting mechanics clarification

I am reading the following paper: http://www.jstor.org/stable/10.1086/587624 and I am confused about one of the definitions at the start of section III. The auther defines $\bar{U} = \sum_{i=m}^n\...
2
votes
0answers
33 views

How does the Borda count work?

I was watching this video. about ranking a bunch of proposals by dividing the full list in to sub lists and each person that submitted the proposals gets one of these sub-lists and ranks it. The lists ...
2
votes
3answers
117 views

How do I weight votes based on number of possible voters?

Scenario: I have a book club that reads a book every month. My website allows the readers to give a 5 star rating to each book. We have 10 members and a rule that a member may only vote on a book they ...
0
votes
0answers
24 views

Optimal voting algorithm for two-person position

Say there is an election for a position filled by two people (e.g. two senators), and n people are running in the race. Considering that preferences may vary (e.g. some people might think candidates ...
4
votes
2answers
181 views

Number of elements in cartesian power with a majority constraint

Problem: I would like to know the number of elements in the cartesian power $X^n$ (cartesian product of one set $X$ by itself, $n$ times) with a majority constraint: how many elements in $X^n$ have a (...
0
votes
1answer
50 views

Understanding the proof of Gibbard-Satterthwaite theorem

Let $n$ be the number of voters and $A$ be the set of alternatives. For voter $i$, we denote by $a \succ_i b$, if $i$ prefers $a$ to $b$, where $a,b \in A$. Let $L(A)$ denote the set of all strict ...
3
votes
0answers
94 views

What is the math behind calling election seats with confidence, before all votes have been counted?

On election night, predictions are made on the winner of each district, after only a fraction of the vote has been counted up. How is this done? Say there is a seat up for election, and 10,000 votes ...
2
votes
1answer
114 views

Anyone know about definition of weak dictator?

I am trying to prove arrow's impossibility theorem in case which ties are allowed in individual preference lists and so is social preference list. It says that if $p$ is a weak dictator, then we can ...
0
votes
0answers
28 views

Difference between set(determined) but unknown result and not yet determined result in terms of probability

Lets say that 44 respondents vote for something, 39 againts and 17 didn't respond or didn't make a decision, yet. Does it change anything in regard to probability that the voting will pass if we know ...
0
votes
1answer
41 views

How to find a quota which makes a voter a dummy voter?

I have four voters: $A$, $B$, $C$, and $D$. \begin{align*} &A\ \text{has}\ 6\ \text{votes}\\ &B\ \text{has}\ 6\ \text{votes}\\ &C\ \text{has}\ 2\ \text{votes}\\ &D\ \text{has}\ 1\ \...
1
vote
1answer
32 views

How many voters can one find in a set?

Recently some german federal states had elections. The news used to say that every n-th voter chose party X. While sitting in the train I was thinking about the following. Someone counts all persons ...
1
vote
1answer
266 views

Which voting method is the most fair? [closed]

I have heard of Plurality Borda Count Instant Runoff Sequential Pairwise voting methods, where it mathematically can be proved which is the most fair and in which situations. From my ...
0
votes
1answer
33 views

Can any information be gathered from the list of people who did or did not vote

I have found out to my surprise that the list of who did or did not vote is publically available in Texas. My question is, can information regarding my preference be ascertained by the fact that I ...
4
votes
1answer
297 views

Violation of the irrelevant alternative criterion of fairness in a pairwise comparison

I am teaching my students about the fairness criteria for voting system, working up towards arrow's impossibility theorem. One of the voting methods is called the pairwise comparison method: voters ...
0
votes
1answer
110 views

Find a voting system - possibly Schulze Method

I remember the Schulze Method from back when I was studying Econ... that was years ago and my math isn't the greatest, go easy on me. We are piloting a project to make a to-do list app for teams, I'm ...
2
votes
0answers
82 views

Proof of two properties of a simple math function

I would like to define a function to evaluate the value for some entities which receive a number of "up"s ($\mathcal{u}$) and "down"s ($\mathcal{d}$). I devised the following function: $\mathcal{f}...
1
vote
1answer
54 views

Condorcet winner and pluralism by 51%

Is it possible for the winner by pluralism to not be the Condorcer winner, if the winner by pluralism wins by 51%? This assumes 3 or more candidates. Also this assumes a rank and or preferential ...
1
vote
1answer
47 views

Are the following two definitions of Borda winner equivalent?

The Borda count is a method used to determine the winner object where people rank objects. For instance, imagine each person ranking 3 objects. The highest ranked object gets 2 points, the second gets ...
0
votes
1answer
44 views

Normalizing votes based on source's rank

If article a from source A has 100 votes, and article b from source B has 10 votes, without simply saying that article a is better because it was voted more, how can I normalize the weight of these ...
3
votes
1answer
780 views

Game Theory Voting

I am having some difficulty in solving the following problem. I was wondering whether someone would be kind enough to sketch a solution or even better to solve the whole game. Thanks Suppose that ...
4
votes
2answers
70 views

Fair continuous election algorithm in a limited set of users

I have an election method in mind, don't know if already exists but I think there must be. It is used in a finite set of users and continuous. Every round, somebody is picked randomly depending on ...
1
vote
2answers
83 views

Calculate the Ranks of Candidates based on Votes and Total Candidates

What is the formula to calculate the rank of each candidate when I have the total candidates and votes secured by each? I've managed the percentage part, but calculating the rank has me stuck. Id be ...
2
votes
1answer
83 views

Counting in Arrow's theorem

I seem to be really confused with the counting system in Arrow's theorem. Can I have a simple explanation how they determine the outcome? I can't determine the outcome using rules from my notes. It ...
2
votes
2answers
112 views

Why not n=2 in Arrow's theorem

Why in the statement of Arrow's impossibility theorem we omit the case n=2? I will appreciate it if you can explain it in easy words. I'm by no means an expert in the area (I think it's very much ...
3
votes
1answer
90 views

Photo Rating System based of Community 'Likes'

I'm hoping to get some assistance from some math gurus on a troubling problem i'm having with a website. The site has a very large gallery (millions of photos) which are uploaded by users. The users ...
1
vote
2answers
83 views

Decide the most favorable candidate

Consider an election voting process where people need to elect a representative among n number of candidates. Is there an approach to determine the most favorable option? Voting just a single person ...
5
votes
1answer
96 views

Introductory text on voting theory

Some years ago I read about a famous theorem by K. Arrow on rank-order voting systems. My interest in voting theory topic has been spurred by the use of MeekSTV in our moderator elections. As such, I'...
3
votes
1answer
95 views

Stability under supremum of sets of social choice function with single peaked preferences

Here is a question emerging from reading Moulin, H. (1980). On strategy-proofness and single peakedness. Public Choice, 35(4), 437–455. The setting is as follows: A non-empty finite set of ...